Traveling waves in integro-difference equations with a shifting habitat

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Li, Bingtuan¹  Wu, Jianhua² 

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710062, Shaanxi, Peoples R China

关键词: Integro-difference equation;    Shifting habitat;    Persistence;    Traveling wave;    Spreading speed;   

DOI  :  10.1016/j.jde.2019.10.018

来源: Elsevier

【 摘 要 】

We study an integro-difference equation that describes the spatial dynamics of a species in a shifting habitat. The growth function is nondecreasing in density and space for a given time, and shifts at a constant speed c. The spreading speeds for the model were previously studied. The contribution of the current paper is to provide sharp conditions for existence of forced traveling waves with speed c. We show the existence of traveling waves with zero value at infinity or -infinity for c in different value ranges determined by the spreading speeds. We also show the existence of a traveling wave with any speed c for the case that the species can grow everywhere. Our results demonstrate the existence of different types of traveling waves with the same speed. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free